What is the ruling on shunning a wife who caused a son to be undutiful to his parents, and is it permissible for the son to draw near to his family without his wife?

Obeying parents has its limits. If the mother's objection to your brother marrying this girl has no legitimate Sharia justification, then obedience to her in this matter is not obligatory. It is better for the family to accept the son's apology if he has erred, and the brother's wife should be allowed to enter the house unless there is an anticipated harm from her.